Inter-track interference cancelation in the presence of frequency offset
An initial phase offset between a center track and a side track is determined. An initial side track pulse shape is determined using the initial phase offset and side track interference. The initial side track pulse shape minimizes a contribution of the side track interference to a center track bit. The contribution of the side track interference is removed from the center track bit using the initial side track pulse shape and the side track interference.
1. A method, comprising:
determining an initial phase offset between a center track and a side track;
using a processor to determine an initial side track pulse shape, using the initial phase offset and side track interference, wherein the initial side track pulse shape minimizes a contribution of the side track interference to a center track bit; and
removing the contribution of the side track interference from the center track bit using the initial side track pulse shape and the side track interference.
2. The method of claim 1 , wherein the center track and the side track are associated with a shingled magnetic recording (SMR) system.
3. The method of claim 1 , wherein determining the initial phase offset includes using
L
^
N
-
1
=
m
^
N
-
1
+
L
2
+
1
,
where {circumflex over (m)} N−1 =arg max m s m N−1 and s m N−1 =Σ i=0 L |C i+m N−1 |.
4. The method of claim 1 , wherein using the processor to determine the initial side track pulse shape includes using a correlation metric C m N−1 =Σ k=1 T y k N b k−m N−1 , where T is a number of samples used for the correlation.
5. The method of claim 1 , wherein determining the initial phase offset includes using
L
^
N
-
1
=
L
max
2
+
1
-
i
max
,
where i max =arg max i ĥ i LMS N−1 and L max is the length of the initial side track pulse shape.
6. The method of claim 1 , wherein using the processor to determine the initial side track pulse shape includes using ĥ LMS N−1 =arg min h N−1 E[|e k 1 | 2 ], where e k 1 =y k N −Σ i=−L max L max h i N−1 b k−i N−1 and L max is the length of the initial side track pulse shape.
7. The method of claim 1 , wherein using the processor to determine the initial side track pulse shape includes using ĥ k+1 LMS N−1 = ĥ k LMS N−1 +μ 1 ×e k 1 × b k N−1 , where e k 1 =y k N −Σ i=−L max L max h i N−1 b k−i N−1 , L max is the length of the initial side track pulse shape, μ 1 is an adaptation coefficient, and b k N−1 =[b k−L max N−1 . . . b k+L max N−1 ].
8. The method of claim 1 , further comprising:
using the processor to determine a second side track pulse shape, using the initial side track pulse shape and the side track data, wherein the second side track pulse shape minimizes the contribution of the side track interference to a second center track bit; and
remove the contribution of the side track interference from the second center track bit using the second side track pulse shape and side track data.
9. The method of claim 8 , wherein using the processor to determine the second side track pulse shape includes using ĥ k+1 LMS N−1 = ĥ k LMS N−1 +μ 5 ×e k 5 × b k N−1 , where e k 5 =y k N −Σ i=−L L h i N−1 b k−i−{circumflex over (L)} N−1 N−1 and μ 5 is an adaptation coefficient.
10. A system, comprising:
a processor; and
a memory coupled with the processor, wherein the memory is configured to provide the processor with instructions which when executed cause the processor to:
determine an initial phase offset between a center track and a side track;
determine an initial side track pulse shape, using the initial phase offset and side track interference, wherein the initial side track pulse shape minimizes a contribution of the side track interference to a center track bit; and
remove the contribution of the side track interference from the center track bit using the initial side track pulse shape and the side track interference.
11. The system of claim 10 , wherein the system is associated with shingled magnetic recording (SMR).
12. The system of claim 10 , wherein the instructions for determining the initial phase offset include instructions for using
L
^
N
-
1
=
m
^
N
-
1
+
L
2
+
1
,
where {circumflex over (m)} N−1 =arg max m s m N−1 and s m N−1 =Σ i=0 L |C i+m N−1 |.
13. The system of claim 10 , wherein the instructions for determining the initial side track pulse shape include instructions for using a correlation metric C m N−1 =Σ k=1 T y k N b k−m N−1 , where T is a number of samples used for the correlation.
14. The system of claim 10 , wherein the instructions for determining the initial phase offset include instructions for using
L
^
N
-
1
=
L
max
2
+
1
-
i
max
,
where i max =arg max i ĥ i LMS N−1 and L max is the length of the initial side track pulse shape.
15. The system of claim 10 , wherein the instructions for determining the initial side track pulse shape include instructions for using ĥ LMS N−1 =arg min h N−1 E[|e k 1 | 2 ], where e k 1 =y k N −Σ i=−L max L max h i N−1 b k−i N−1 and L max is the length of the initial side track pulse shape.
16. The system of claim 10 , wherein the instructions for determining the initial side track pulse shape include instructions for using ĥ k+1 LMS N−1 = ĥ k LMS N−1 +μ 1 ×e k 1 × b k N−1 , where e k 1 =y k N −Σ i=−L max L max h i N−1 b k−i N−1 , L max is the length of the initial side track pulse shape, μ 1 is an adaptation coefficient, and b K N−1 =[b k−L max N−1 . . . b k+L max N−1 ].
17. The system of claim 10 , wherein the memory is further configured to provide the processor with instructions which when executed cause the processor to:
determine a second side track pulse shape, using the initial side track pulse shape and the side track interference, wherein the second side track pulse shape minimizes the contribution of the side track interference to a second center track bit; and
remove the contribution of the side track interference from the second center track bit using the second side track pulse shape and side track data.
18. The system of claim 17 , wherein using the processor to determine the second side track pulse shape includes using ĥ k+1 LMS N−1 = ĥ k LMS N−1 +μ 5 ×e k 5 × b k N−1 , where e k 5 =y k N −Σ i=−L L h i N−1 b k−i−{circumflex over (L)} N−1 N−1 and μ 5 is an adaptation coefficient.
19. A computer program product, the computer program product being embodied in a non-transitory computer readable storage medium and comprising computer instructions for:
determining an initial phase offset between a center track and a side track;
using a processor to determine an initial side track pulse shape, using the initial phase offset and side track interference, wherein the initial side track pulse shape minimizes a contribution of the side track interference to a center track bit; and
removing the contribution of the side track interference from the center track bit using the initial side track pulse shape and the side track interference.
20. The computer program product of claim 19 , wherein the center track and the side track are associated with a shingled magnetic recording (SMR) system.